10y^2+33y+20=0

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Solution for 10y^2+33y+20=0 equation:


Simplifying
10y2 + 33y + 20 = 0

Reorder the terms:
20 + 33y + 10y2 = 0

Solving
20 + 33y + 10y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(5 + 2y)(4 + 5y) = 0

Subproblem 1

Set the factor '(5 + 2y)' equal to zero and attempt to solve: Simplifying 5 + 2y = 0 Solving 5 + 2y = 0 Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2y = 0 + -5 2y = 0 + -5 Combine like terms: 0 + -5 = -5 2y = -5 Divide each side by '2'. y = -2.5 Simplifying y = -2.5

Subproblem 2

Set the factor '(4 + 5y)' equal to zero and attempt to solve: Simplifying 4 + 5y = 0 Solving 4 + 5y = 0 Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 5y = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5y = 0 + -4 5y = 0 + -4 Combine like terms: 0 + -4 = -4 5y = -4 Divide each side by '5'. y = -0.8 Simplifying y = -0.8

Solution

y = {-2.5, -0.8}

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